TN295 
.U4 

No. 9031 






"O. AT ^^VrMTk*" «*> «i *ft^^i,*„ 'TIS /SkT .* 



.V 



./x 



:.' .*^'*-, • 



V ■'*.^* 
















,^ 



'- "L 



' ' ♦' 







-^^d^ 

.^^°- 













• >^"V. '• 







.^°- 



O. * , , 



< o 



,0"' ^^ '* 









,^^ ^^. 



*' .♦''♦. 



'?^^ ^J* o^t 






•' '=^..*^ 



.- **"*« ■•.' 



.,. ^^v --^ .J</^W' >' "#. •.?^^.' *' ■'* 



hi" 'V / ." 



'.•i;;^-\ 0°*.^^^.% ,**.C^.\ <.°*.i^^.'\ /.-i.;^.*-?, /.i^^Jl."^ 










\ 









>•' V 







;-• ,e.°-n..J-^;^,.^°-, -.« 











^»^^^"^^ ^^^^" ^^^% °-w^*" /\ '.^K*" ^^'V • 







.o-n*. '. 



>"'^^. 



\ 



<<•. c*^ 



^V- . . "^ * o « o ■■ <; 



-i-*^ c^k^feC!. -^ 










'e^ A^" *>^^/):^„ %. j^^ - 



° ^^^^ "'JiR': '^^'^^ «^W%t -^^^ » 







'. -t. 



^v^o^ 



" V^ •'.»<'..,. .v°'" -"*"-•. ■'■^' 













r* A 



/X 



*' °^ .'^^ /! 






'bV 






"oV" 

























-X ".o^V.-.^o 



r* A 




*. .« .-^wv. ^^^^' 














•^^ ^° '^i:-. °^ a^^ 




...., ^^ 



.•*' »! 



• X.^* •'^■- *W* .-^te": %.<*^ ." 



























I': *W* 



/°- 



0^ oo""*^^© 



%, 




v.^^^ 








^^-n^. 



























•^v^^^ 

c^^. 














;•' ^0^ 



^^ 'I 




.^*^°- 






















.,% 














^* r^0 











.^^\ 




> V 










x/ 
**^% 
















3' *, 





I,'-. ■%.,^'' ' 







•o "Pa a"* 




ft? ^A 











<^ . 





■'/> 





\ 






*bv" 



*^'. V 







^ >. c-^' 



^^^9^^ 

.^^'V 
V ^ 





































-^^0^ 







0^ .r^% ^^ 




-01.-' 










m^ , N o « 



'0/ 




**'% 








•j^ & ♦J 












i^r-^ """ v^" •- ^' 







^'-^.^ 



nV V 






r *i 















' .*' 












=ef>. ^<5' 











•n^-o* 



















o V 



* .^' 




^^-n^ 



,*^% V 









-^^0^ 






'-> '- v^* .....\ 











^V" 





^v^' 












J^ 9031 



Bureau of Mines Information Circular/1985 



Computer Program for Calculating 
Gravimetric Primary Standard 
Gas Mixtures 



By Ernest W. Loya 




UNITED STATES DEPARTMENT OF THE INTERIOR 



,T5J 

'V/NES 75TH AV*^ 



Information Circular 9031 



Computer Program for Calculating 
Gravimetric Primary Standard 
Gas Mixtures 



By Ernest W. Loya 




UNITED STATES DEPARTMENT OF THE INTERIOR 

Donald Paul Hodel, Secretary 

BUREAU OF MINES 
Robert C. Norton, Director 



TV! 0.^9 




Library of Congress Cataloging in Publication Data: 



Loya, Ernest W 








Computer program for calculating gravimet 


ric primary 


standard 


gas 


mixtures. 








(Information circular /United States Department of the 


Interior, 


Bu- 


reau of Mines ; 9031) 








Bibliography: p. 7-8. 








Supt. of Docs, no.: I 28.27:9031, 








1. Gases— Analysis— Computer programs. I. 


Title. 11. 


Series: Infor- 


mation circular (United States. Bureau of Mines) 


; 9031. 






TN295.U4 [QD121] 622s [544'. 4] 


85-600064 





4 

O CONTENTS 

^ Page 



1 



""■v^ 



Abstract 1 

/^introduction 2 

r^ Acknowledgments 2 

VJ Method of calculation 2 

Buoyancy correction 2 

Final composition 3 

Standard error 4 

Program description 6 

Input 6 

Output 7 

References 7 

Appendix A. — Computer program listing for PRISTD 9 

Appendix B. — Flow chart for computer program PRISTD 17 

Appendix C, — Sample calculation of gravimetric primary standard mixture 30 

Appendix D. — Nomenclature 34 





UNIT OF MEASURE ABBREVIATIONS 


USED IN 


THIS REPORT 


°c 


degree Celsius 


kg 


kilogram 


g 


gram 


mg 


milligram 


g/mL 


gram per milliliter 


mL 


milliliter 


g mol 


gram mole 


mm Hg 


millimeter of mercury 


K 


kelvin 


% 


percent 



COMPUTER PROGRAM FOR CALCULATING GRAVIMETRIC 
PRIMARY STANDARD GAS MIXTURES 

By Ernest W. Loya ^ 



ABSTRACT 

The Bureau of Mines has developed a computer program for calculating 
the composition of gravimetric primary standard gas mixtures. The For- 
tran IV program applies corrections due to buoyancy variations of the 
cylinder and inaccuracies of the balance weights. The program also de- 
termines the statistical error due to the sensitivity and precision of 
the balance and applies the analytical error of the weighed gases. 



Chemist, Helium Field Operations, Bureau of Mines, Amarillo, TX. 



INTRODUCTION 



This report describes a computer pro- 
gram developed to determine the content 
and associated statistical error of grav- 
imetric gaseous mixtures prepared by the 
Bureau of Mines. In the production of 
helium, the Bureau uses the primary stan- 
dard mixtures to calibrate analytical in- 
struments, determine their accuracy and 
verify their precision. 

Previous reports have dealt primarily 
with mixture preparation techniques and 
descriptions of the calculation procedure 
(1-2). 2 Subsequently, computer technol- 



ogy has permitted the performance of com- 
putations with higher efficiency and ac- 
curacy. The algorithm was developed to 
improve the quality and accuracy of the 
standard mixtures and to relieve the ana- 
lyst from the tedious mathematical mani- 
pulations required. 

The program is written in Fortran IV 
for a computer with 64,000 bytes of core 
and auxiliary disk storage. A cathode 
ray tube (CRT) terminal is used to enter 
the input data. The output is printed on 
a 600-line-per-minute printer. 



ACKNOWLEDGMENTS 



The author extends his appreciation to 
Betty A, Lowe, chemist. Helium Field Op- 
erations, for her invaluable assistance 
and suggestions in modifying and prepar- 



ing the computer program. Recognition is 
also given to Marvin L. Burfield, a form- 
er employee, for developing the algorithm 
and writing the original program. 



METHOD OF CALCULATION 



The following equations are utilized in 
the program to determine the buoyancy 
correction, final composition of the mix- 
ture, and standard error (standard devia- 
tion of the mean) (3^). 

BUOYANCY CORRECTION 

The buoyancy correction is calculated 
for each cylinder weighing. Buoyancy is 
the product of ambient air density and 
volume of the cylinder. The correction 
is determined from the difference of the 
buoyancies due to the cylinder and the 
utilized weights, as shown by the 
following: 



B = D^V, 



DwVw, 



(1) 



where B = buoyancy correction, g. 



density of air in balance 



weighing chamber 
chamber), g/mL, 

cylinder volume, mL, 



(upper 



^Underlined numbers in parentheses re- 
fer to items in the list of references 
preceding the appendixes. 



and 



D^ = density of air in balance 
weight chamber, (lower cham- 
ber), g/mL, 

V^ = volume of utilized weights, 
mL. 



Air density is the sum of the densities 
of ambient dry air and water vapor. Den- 
sity, as given below, is determined from 
temperature, relative humidity, and baro- 
metric pressure measurements obtained 
from bimetal centigrade thermometers, 
direct-reading hygrometers, and a mercu- 
rial barometer, respectively. 

D = (M^/Vj„)(Tg/T)[(F - RVp)/Pg] 

+ (M„/V^)(Tg/T)(RVp/Pg), (2) 

where D = density of ambient air, g/mL, 

M^ = molecular weight^ of air, g, 

P = barometric pressure, ram Hg, 

^Reference to molecular weight, atomic 
weight, and moles in this report are in 
gram units, i.e., molecular weight refers 
to gram-molecular weight, etc. 



R = relative humidity, 

Vp = vapor pressure of water, mm 
Hg. 

Tg = Standard absolute tempera- 
ture, K, 

M^ = molecular weight of water, g, 

Vj^ = molar volume of ideal gas at 
standard conditions, mL, 



and N = total number of added gases. 

Moles of each component are the quo- 
tient of the mass added of component i 
from each gas j and the molecular or 
atomic weight of component i, as given by 
the following: 



Mi,j = Gi^j/Y, 



(5) 



where G^^ ^ = mass of component i in gas 
J, g, 



Pg = standard barometric pressure, 
mm Hg, 

and T = absolute temperature, K, 

Vapor pressure of water is determined 
from an empirical approximation of the 
Clausius-Clapeyron equation, which cor- 
relates the variation of vapor pressure 
with temperature (4-5). 



and 



T 



(3) 



where Vp = vapor pressure of water, mm 
Hg, 



A = -5305.041903, K, 

C = 20.96094276, constant of 
integration, 

and T = absolute temperature, K. 

FINAL COMPOSITION 



Yj^ = molecular or atomic weight 
of component i, g. 



Mass of added component i in gas j is 
the product of the weight fraction for 
component i and mass of added gas j, as 
given by the following: 



• = F- W- 



(6) 



where F^ = weight fraction of component 

and W^ = mass of gas j , g. 

Weight fraction of component i per gas 
j is determined from the following 
equations: 



12 
Fi = ^i/.Z^Zi, 



Zi = XiYi 



(7) 



(8) 



where Xj^ = mole fraction of component i 
in gas j , 



The final composition in mole fraction 
of each component is the quotient of the 
total moles of a component and the total 
moles of att components in alt added 
gases. 

N N 12 
Ci =.E M. j/_E E Mi j, 

3 = 1 '-■ j = li=l '-" (4) 

where C^ = mole fraction of compo- 
nent i, 

M^ • = moles of component i in 
gas j , g mol. 



and YjL = molecular weight or atomic 
weight of component i, g. 

Mass of gas j is the difference of the 
average mass determinations of the cylin- 
der in the applicable weighing sessions k 
and k + 1, as given by the following: 



^1 - %+1 ~ hi 



(9) 



where R-^ = average mass of cylinder 
for weighing session k, g. 



and 



k + 1 



average raass of cylinder 
for weighing session k + 

1, g. 
Average mass of the cylinder for a 
weighing session is the quotient of the 
sum of the mass determinations and the 
number of determinations as given by the 
following: 



N 



N i^l^i' 



(10) 



and 



mass determination i for 
weighing session k, g, 

total number of mass deter- 
minations of cylinder for 
weighing session k. 



Each mass determination is the algebra- 
ic sum of the average balance zero value, 
the determined buoyancy correction, and 
the corresponding correction factor due 
to the inaccuracies of the balance 
weights with the nominal mass measurement 
of the cylinder, as shown below: 



standard error of each weighing session. 
The following description begins with the 
equation for mole fraction standard 
error. The variables and data required 
for each equation are presented. 

Mole fraction standard error for each 
component is calculated from propagation 
of error combinations of the standard 
errors due to the precision variance of 
the balance and analysis error of the 
gases. Standard error is the square root 
of the standard error variance, as given 
by the following: 



where 



^c. -''V' 



(12) 



12 12 

S2 = (1/.^ M. )^{S2 [(.^ M. ) - M. ]2 



i=l i 



i=l 1 



12 



-"fi^iSiSi>-=iiJ. 



(13) 



mole fraction standard er- 
ror of component i. 



Ri = R^ - [(Zj. + Z^+i)/2] + B + F, (11) 

where R^. = nominal mass measurement of 
the cylinder, g, 

Zj. = balance zero measurement, g, 

B = buoyancy correction, g, 

and F = balance weights inaccuracy 
correction factor, g, 

STANDARD ERROR 

The following describes the statistical 
error determination (mole fraction stan- 
dard error) for each component. Final 
error variations are calculated from two 
sources: the precision variation (stan- 
dard error) of the balance and the ana- 
lytical error determined for each compo- 
nent of the gases. The program calcu- 
lates the mean, standard deviation, and 
standard error for each weighing session. 
Analytical errors are entered and statis- 
tically combined with the calculated 



and 



Mi = total moles of component i, 
g mol. 



>j^j = standard error of Mi , g 
i mol. 



The standard error of the total moles 
of component i is the error propagation 
combination of the standard error of the 
total mass added of component i and the 
molecular or atomic weight standard er- 
ror. However, the standard error for the 
molecular or atomic weight is compara- 
tively small and is considered zero, the 
expression for s2 is simplified as shown 

Mi 

in equation 16 below. 



S2 = (S2 /y2) + (g2s2 /YJ) , d^) 
1 Y-i 1 





Mi ^ Gi i 


since 


\ = 0. 


then 


^^i = VI 



(15) 
(16) 



and 



1 mass of component i, g, 



= standard error for the mo- 
lecular or atomic weight 
of component i, g, 



of component i, g. 



Standard error for total mass of compo- 
nent i is a summation of the standard er- 
rors determined for the mass added of 
component i per gas j , as given by the 
following: 



'I 






(17) 



Zi = XiYi 



(20) 



where X^ = mole fraction of component i 
in gas j . 

Yj^ = molecular or atomic weight 
of component i, g, 

and S2 = standard error of Z^ , 
i 

The standard error of Z^ is determined 
from the error propagation combination of 
the standard error of the mole fraction 
of component i in gas j and the molecular 
or atomic weight standard error. How- 
ever, since S^ =0 (see equation 15), 

then S2 is reduced to equation 22 as 

^i 
shown below: 



where Sq = standard' error for mass 
i'j of component i in gas j. 

The standard error for mass of conq)0- 
nent i in gas j is determined by the fol- 
lowing expression: 



S2 = s2 W? + f2s2 , 



(18) 



i/D 



where Sp = weight fraction standard 
i error for component i, 



S2 = y2s2 + X2s2 , (21) 

^ , X A . 1 I . 

Ill 



'I'^W' 



(22) 



^ fraction of component i in 
gas j, 

and Sy = standard error for the mo- 
i lecular or atomic weight 
of component i, g. 



W^ = mass of gas j, g, 

F^ = weight fraction of compo- 
nent i. 



and St.7 = standard error for mass of 



^ gas j, g. 



The standard error for the mass of gas 
j is calculated from the error propaga- 
tion of the average mass of the cylinder 
determined in weighing sessions k and 
k+1, as given by the following: 



S2 = si + s2 



(23) 



Weight fraction standard error for com- 
ponent i is calculated from the following 
equations (6): 



where S^ = standard error for average 
^ mass of cylinder for 

weighing session k, g. 



12 12 

S2 = (1/ Z Z.)4(s2 [( z z.) - Z.]2 

F i=i 1 Z i=i 1 1 



+ Z2[( E%2 ) _ s2 )]}, (19) 
1 1=1 \ \ 



and S^ = standard error for aver- 
^"•"^ age mass of cylinder for 
weighing session k+1, 
g. 

Standard error for the mass of the cyl- 
inder is calculated from the following: 



S2 = .^(R - R.)2/N(N - 1) 
R^ 1=1 k X 



(24) 



Rj^ = mass determination i of cyl- 
inder for weighing session 
k, g. 



where R^^ = average mass of cylinder for and N = total number of mass deter- 
weighing session k, g, minations of cylinder for 

weighing session k. 



PROGRAM DESCRIPTION 



Item 3a-3g: 



Item 4a-4c: 



The program, labeled PRISTD, is written Item 1: 
to use double precision floating-point 
arithmetic to perform all calculations. 
Dimension statements limit the number of 
gas additions to six and the number of Item 2: 
weighing sessions and weighings per ses- 
sion to seven. The computation deter- 
mines the mole fraction for a maximum of 
12 components. Atomic and molecular 
weights for the nine normally utilized 
components appear in the program. A max- 
imum of three additional components and 
their associated atomic or molecular 
weights may be entered as required. The 
input data is coded on specifically pre- 
pared data sheets and entered by use of a 
CRT terminal. 

Requisite computation data are recorded 
from instrumentation used in the prepara- 
tion of the standard mixtures. All the II. 
weight determination data are acquired 
from a high-capacity, substitution-type 
balance. Buoyancy variations are deter- 
mined by computing air density and the 
external volumes of the cylinder and uti- 
lized weights. 

Air density is computed from data 
gathered by measuring the following ambi- 
ent conditions: temperature, relative 
humidity, and barometric pressure. The 
external cylinder volume is determined by 
a gravimetric measurement of water dis- 
placement. The volume of the weights is 
calculated from density data supplied by 
the manufacturer. 

The computer program listing for PRISTD 
is given in appendix A and flow chart is 
illustrated in appendix B. 



Identifying information, 
maximum of 66 alphanu- 
meric characters, 66A1 
format. 

Number of weighing ses- 
sions specified in in- 
teger numbers, II 
format. 

Number of weighings per 
session specified in 
integer numbers, II 
format. 

Chemical symbol and mo- 
lecular weights of ad- 
ditional optional com- 
ponents specified in 
alphanumeric and real 
numbers, A4 and FIG.G 
format, respectively. 
Mass and buoyancy determination data 
recorded for each weighing. 



Item 1 



Item 2; 



Item 3: 



Item 4; 



Item 5: 



INPUT 

The following describes the 
tered using a CRT terminal. 
I. Program identification and 
parameters. 



input en- 
control 



Item 6: 



Weight readings, speci- 
fied in real numbers, 
FIG.G format. 

Zero balance readings 
specified in real num- 
bers, F1G,G format. 

Temperature readings re- 
quired for correction 
of mercurial barometer 
readings specified in 
real numbers, F1G,G 
format. 

Barometric pressure 
readings specified in 
real numbers, F1G,G 
format. 

Relative humidity read- 
ing of balance upper 
chamber specified in 
real numbers, F10,G 
format. 

Relative humidity read- 
ing in balance lower 
chamber specified in 



real numbers, FIO.O 
format. 
Item 7: Temperature reading in 
balance upper chamber 
specified in real num- 
bers, FIO.O format. 
Item 8: Temperature reading in 
balance lower chamber 
specified in real num- 
bers, FIO.O format. 
Item 9: Displacement volume 
measurement of cylin- 
der specified in inte- 
ger numbers, 110 
format. 
Item 10: Counterbalance weight 
of cylinder specified 
in integer numbers, 
110 format. 
III. Composition data of the gases in 
mole fraction and respective error 
deviation are entered for the 
following components: helium, 
hydrogen, neon, nitrogen, methane, 
oxygen, argon, carbon dioxide, 
helium-3, and a maximum of three 
additional optional components. 
Each of these data items are 
specified in real numbers, D20.10 
format, 

OUTPUT 

A previously composed heading (INPUT, 
I, Item 1:, see page 6) is printed at 
the top of the initial and final output 
pages. Subsequent to the initial head- 
ing, all the entered input is printed al- 
lowing for verification and reference. 
The printed calculated results are listed 
in the next column. 



I, Computation of interim values and 
buoyancy correction 

A, Barometric pressure in real num- 

bers, 8F10.3 format. 

B, Vapor pressure of water in bal- 

ance upper chamber in real num- 
bers, 8F10.3 format. 

C, Vapor pressure of water in bal- 

ance lower chamber in real num- 
bers, 8F10.3 format, 

D, Air density upper chamber in 

real numbers, 3E12,5 format, 

E, Air density lower chamber in 

real numbers, 3E12,5 format, 

F, Buoyancy of cylinder in real 

numbers, 3E12,5 format, 

II, Computation of cylinder mass 

A, Mass of cylinder (after applic- 

ation of all corrections and 
zero value subtraction) in real 
numbers, 8F10,4 format, 

B, Average mass of cylinder for 

weighing session in real num- 
bers, F10,4 format, 

III, Computation of final results 

A. Previously composed heading 

(INPUT, I, Item 1:, see page 6) 
printed in alphanumeric char- 
acters, 66A1 format, 

B, The final calculated results are 

printed in five columns labeled 
"CONCENTRATION, STANDARD ERROR, 
RELATIVE ERROR, MOLE FRACTION, 
and STANDARD ERROR" for each 
component. All the values are 
in real numbers with formats of 
F15,5, F15,5, F15,5, E16,10, 
and E16,10, 
Sample output data are demonstrated in 
appendix C of this report. 



REFERENCES 



1, Loya, E, W, , C, A, Seitz, and D, E, 
Emerson, Gravimetric Preparation of Pri- 
mary Standard Gas Mixtures in the Parts 
Per Trillion Range. BuMines RI 8643, 
1982, 4 pp. 

2. Miller, J. E., A. J. Carroll, and 
D. E. Emerson. Preparation of Primary 
Standard Gas Mixtures for Analytical In- 
struments, BuMines RI 6674, 1965, 10 
pp. 



3, Barford, N, C, Experimental Mea- 
surements: Precision, Error, and Truth, 
Addis on-Wes ley (London), 1967, pp, 35- 
37, 

4. National Research Council of the 
United States of America, International 
Critical Tables of Numerical Data, Phys- 
ics, Chemistry and Technology, McGraw- 
Hill, V, III, Isted,, 1928, pp, 210- 
212, 



5. Prutton, C. F., and S. H. Maron, 
Fundamental Principles of Physical Chem- 
istry. Macraillan, 1951, pp. 91-95. 

6. Meyer, S. L. Data Analysis for 
Scientists and Engineers. Wiley, 1975, 
pp. 39-48. 

7. Brombacher, W. G. , D. P. Johnson, 
and J. L. Cross. Mercury Barometers and 
Manometers, U.S. Dep. Commerce, NBS Mono- 
graph 8, May 20, 1960, pp. 4, 27-28, 33. 

8. Dalton, B. J. Local Value of Ac- 
celeration of Gravity at the Helium 



Research Center (Potsdam System). Helium 



43, 



April 



Res. Center Memorandum Rep, 

1964, 13 pp.; available from Helium Field 

Operations library, Amarillo, TX. 

9. CRC Press. CRC Handbook of Chem- 
istry and Physics, Cleveland, OH, 57th 
ed., 1976, 2390 pp. 

10. McCracken, D. D. A Guide to For- 
tran IV Programing. Wiley, 2d ed. , 1972, 
288 pp. 



APPENDIX A. —COMPUTER PROGRAM LISTING FOR PRISTD. PROGRAM CALCULATES COMPOSITION 
AND ERROR OF GRAVIMETRIC PRIMARY STANDARD GAS MIXTURES 

c* * 

C* PRISTD ♦ 

C* * 

(;**♦♦♦*♦**♦♦****♦*♦♦*♦*******♦**************♦**************♦********** 

C 

C *** THIS PROGRAM CALCULATES THE MOLE FRACTION, STAMDi\RD ERROR, AMP 

C *** RELATIVE ERROR FOR NINE COMPONENTS - He H2 Nf N? CH'+ 02 

C *** AR C02 HE3 - OF GRAVIMETRIC STANDARD MIXTURES PREPARED 

C *** BY SECTION OF TECHNICAL AND ANALYTICAL SERVICES. OPTION TO 

C *** DETEpyilNE THE RESULTS FOR THREE ADDITIONAL COMPONEMTS IS 

C *** PROVIDED. 

C 

C****************************** SECTION A it*************************** 

c 

C *** SECTION A SPECIFIES AND ASSIGNS VARIABLES AND MOST OF THE 

C *** CONSTANTS USED IN THE PROGRAM. 

C 

REAL M 

INTEGER COMPID,DaTaOK,WW,VC 

DOUBLE PRECISION A »C ♦ M , S ,CA iCB »CC ,CD ,CG tCT, Z , RELERR , 

* AIJtWY,XfXY,Y,ZCfCON»TO,RHWtAWC»BY,TB, 

* DC«DWtDWS«FM,H,RHC«S2Fl>'fS2W,S2WF»S2WGtS2WK» 

* S2WY,S2XY,SLIMWY,SUMXY,SUSPWK,SUS2WY,SUS2XY»SX,Tc» 

* TW»VPC«\/PW,Kl«WC,WF,WG,WK«WSlfWS2»WS.^,WS^ 
DIMENSION WSl(ll) ,WS2(10) ,US3(10) tWStdO) , IHF AD ( 66 ) » JJ ( 8 ) , 

* H(7) ,RHC(7) ,PHW(7) tTCC?) fTW(7) ,VPC(7) » VPW ( 7 ) , WC( 7 ) » 

* ZC(8) »S2WG{8) fWY(l?),AWC(e),DWS(3)tW(8) ,S^'-I(8) , 

* WG(8) »y(8»l2) ,SX(e,l2) ,FM(12) ,Y(l2) »TB{^) » 

* S2WY(12),S2FM{12) ,SUS2WK(12) ,C0MplD(l2) ,RELERR(12) 
DATA A,C,S/-530 5.0m90 3,20,g609t276,1.8'+E-5/» 

* CA,CB,CC,CD/1.81tm01E-4,7.0l6E-9,2.8625E-ll,2,617E-m/, 

* WSl, WS2, WS3,WS4/0... 0185 t. 017 i.OSMt.O^lt, . 0636 ,. 0707, . 0802 » 

* .1042,. 1185,. 1 318,. 0,. 0021,, 0016,. 00^7,. 00 76,. 0099,. OlOf, 

* .0121, .0108, .0131, .0,-. 0001, -. 0002 ,-, OOOl ,-. 0002 ,-. 0005 , 

* . 0007, -.0008,, 0019,. 00 2?,. 0,-. 0001, -.000«|,-. 0007, -.0002, 

* -.0004, -,0004,. 0003,. 0007,. 000 3/, 

* COhPID/'HE* , •H2» ,»NE* , •N2' ,»CH4« , •02',«AR« ,*C02» ,'HE3» , 

* » » , » ♦ , » ♦ / 

Yd) = 4,0026 

Y(2) = 2,01594 

Y{?) = 20.183 

Y(4) = 28.0134 

Y(5) = 16.04303 

Y(6) = 31.9908 

Y{7) = 39.948 

Y(8) = 44.00995 

Y(9) = 3,0160 

T0=273.15 

C0N = 273 .15/(22413, 83*760 . ) 



c 


*** 


THEAD 


c 


*** 


MAXI 


c 


*** 


JJ 


c 


*** 


CnMPID 


c 


**♦ 


Y 


c 







10 



ion CONTINUE 

c 

C*****************************NOTE ***♦*****♦♦*♦******♦*********♦**♦*♦ 

C *♦* ALL CONSOLE ENTERED INPUT DATA MUST BE PrEcEDED BY TWO BLANK 

C *** SPACES, THIS IS NEEDED FOR THE DATA TO COINCIDE WITH THE FIELD 

C *♦* DESCRIPTOR INSTRUCTIONS OF THE READ FORMAT STATEMENTS. THIS 

C **♦ REQUIREMENT WAS ESTABLISHED TO ADAPT THE PROGRAM FOR USE WITH THE 

C *♦♦ PERKIN-ELMER DATA SYSTEMS MODEL llOO TERMINAL, 

C 

C****************************** SECTION B **************************** 

c 

C *** SECTION B REQUESTS INPUT DATA FOR THE FOLLOWING! 
COMPOSED HEADING 
NUMBER OF WEIGHING SESSIONS 
NUMBER OF WEIGHINGS PER SESSION 
CHEMICAL SYMBOL FOR ADDITIONAL COmPONENT(S) 
ATOMIC OR MOLECULAR WEIGHT FOR ADDITIONAL COMPONENT(S) 

WRITE(2»3000) 

READ(2t3001) (IHEaD(I) f 1=1 ♦66) 
200 WRITE(2«3002) 

READ(2.3039)MAXI 

IF(MAXI.LE,7,AND.MAXI,GE.l) GO TO 101 
WRITE(2»3003) 
GO TO 200 

101 CONTINUE 
DO 102 I=1,MAXI 
WRITE(2t300H) 
READ(2«3039) JJ(I) 

102 CONTINUE 

103 CONTINUE 
DO lot J=10tl2 
WRITE(2»3005) 
RFAD(2t30 37)COMPTD( J) 
WRITE(2«3006) 
READ(2»3012)Y(J) 

lOU CONTINUE 

WRITE(2.3007) 

READ(2»300a)DATAoK 

IF(DATAOK.GT,0) GO TO 103 

DO 105 J=l,12 

SUS2WK{ J)=0 

S2WY(J)=0. 

WY(J)=0 
105 CONTINUE 

SnMWY=0 

WG(1)=0 

S?WG(1)=0 

WRITE(3,3038) 

WRITE(3t30 0l) (IHEAD(I) .1=1*66) 

WRITE (3*3018) MAX It ( JJ(I) » 1 = 1 « MAX I) 

WRITE (3* 30 09) (COMPID(J) ,J=10tl2) 

WRITE(3»3010) (Y( J) .J=10,12) 



11 



c 

*** 

**♦ 

*** 
*** 
*** 
*** 
*** 
*** 
*** 
*** 
»** 

*♦* 
*** 
♦ ♦4c 
*** 
**♦ 
*** 
*** 
*** 
*♦* 
*** 
*** 
*** 
*** 

*** 
*** 
*** 
*** 
»♦♦ 
*** 



***************************************************************** 

************************* SECTION C ***************************** 



10 

201 



20? 



203 



SECTION 

EACH WEI 

WC - 

ZC - 

TB - 

H - 

RHC - 

RHW - 

TC - 

TW - 

VC - 

WW - 

VPC - 

VPW - 

X - 
sx - 

DWS 

DC 

DU 

BY 

AWC 

S2W 

WG 

S2WG 

XY 

S2XY 

SIIS2XY 

SUMXY 

WF 

WK 

WY 

SUMWY 

S2WF 

S2WK 

SIIS2WK 



C REQUESTS iNPuT DATA AIMQ/OR CALCULATES THE FOLLOWING FOR 
GHING session; 

- BALANCE WEIGHT MEASUREMENTS S CaLC. MaSS OF CYLINDER 

- BALANCE ZERO READINGS 

- BAROMETER TEMPERATURES 

- BAROMETER READINGS X CALC BAROMETRIC PRESSURES 

- RELATIVE HUMIDITIES OF BALANCE UPPER CHAMBER 

- RELATIVE HUMIDITIES OF BALANCE lOwEP CHAMBER 

- TEMPERATURES OF BALANCE UPPER CHAMBER 

- TEMPERATURES OF BALANCE LOWER CHAMBER 

- WEIGHING CYLINDER DISPLACEMENT VOLUME 

- COUNTER BALANCE WEIGHT 

- CaLC. H20 VAPOR PRESSURES OF BALANCE UPPER CHAMBER 

- CALC. H20 VAPOR PRESSURES OF BALANCE LOWER CHAMBER 

- MOLE FRACTION OF COMPONENT J 

- ERROR DEVIATION OF X 

- CALC. CORRECTION FOR INACCURACY OF BALANCE WEIGHTS 

- CALC. AIR DENSITIES OF BALANCE UPPER CHAMBER 

- CALC. AIR DENSITIES OF BALANCE LOwER CHAMBER 
BUOYANCY CORRECTIONS 
AVERAGE MASS OF CYLINDER 
VARIANCE OF AWC 



CALC 
CALC 
CALC 
CALC 
CALC 
CALC 
CALC 
CALC 
CALC 
CALC 
CALC 



MASS OF GAS 

VARIANCE OF WG 

WEIGHT OF COMPONENT J 

VARIANCE OF XY 

SUMMATION OF S2XY»S 

SUMMATION OF XY»S 

WEIGHT FRACTION Op COMPONENT J 

MASS OF COMPONENT J 
CALC. MOLES OF COMPONENT J 
CALC. SUMMATION OF WY'S 
CALC. VARIANCE OF WF FOR COMPONENT J 
CALC. VARIANCE OF WK FOR COMPONENT J 
CALC. SUMMATION OF S2WK»s 



DO 113 I=1»MAXI 

IJ=JJ(I) 

IJ1=IJ+1 

AIJ=IJ 

WRTTE(2,3020) 

WRITE(2»3011) 

READ(2»3012) (WC( J) f J=ltIJ) 

WRITE(2»3007) 

RFAD(2»3008)DATAOK 

IF(DATAOK.GT,0) GO TO 201 

WRITE(2»3021) 

WRITE{2»3011) 

READ(2t3012) ( ZC ( J ) « J=l » I Jl ) 

WRITE(2»3007) 

RFAD(2«3008)DATAOK 

IF(DATAOK.GT,0) GO TO 202 

WRITE(2»3031) 



12 



WRITE(2.3011) 

RE'AD(2»30l2)(TB(J)»J=liIJ) 

WRITE(2»3007) 

RFAD(2f3008)DATAOK 

IF(DATAOK.GT,0) GO TO 203 
20U WRITE(2t3022) 

WRITE(2»3011) 

RE AD (2. 30 12) (H(J)»J=1«IJ) 

WRITE(2»3007) 

READ<2i3008)DATAOK 

irCDATAOK.GT.O) GO TO 20«f 
205 WRITE(2.3025) 

U'RITE(2»3011) 

READ (2 t 3012) (RHC( J) ♦J=1«IJ) 

WRITE(2«3007) 

READ(2»3008)DATAOK 

IF(DATAOK.GT,0) GO TO 205 
20A WRITE(2«3026) 

WRITE(2»3011) 

READ(2i3012) (RHW(J) «J=1«IJ) 

WRITE(2»3007) 

READ(2t3008)DATAOK 

IF(DATAOK.GT,0) GO TO 206 
207 WRITE(2t3023) 

WRITE(2»3011) 

READ (2*30 12) (TC ( J ) » J=l t I J ) 

WRITE(2t3007) 

READ(2»3008)DATAOK 

IF(DATAOK.GT,0) GO TO 207 
20fl WRITE(2»302H) 

WRITE(2t3011) 

READ (2*3012) ( TW ( J ) » J=l » I J ) 

WRITE(2f3007) 

READ(2t3008)DATAoK 

IF(DATAOK.GT,0) GO TO 208 
209 WRTTE(2»3013) 

READ(2»30«+0)VC 

WRITE{2f3007) 

RFAD(2i3008)DATAOK 

IF(DATAOK.GT,0) GO TO 209 
2in WRITE(2»301H) 

READ(2»30^0)WW 

IF(WW,GE,1) GO TO 106 

WRITE(2»3035) 

GO TO 210 
106 CONTINUE 

WRITE(2»3007) 

READ(2«3008)DATAOK 

IF(DATAOK.GT.O) GO TO 210 

WRITE(3»3019)I 

WRITE (3 ♦3020) (WC(J) »J=1»IJ) 

WRITE(3.3n2l) (ZC( J) »J=l»IJl) 

WRITE(3«3022) (H( J) tJ=l»IJ) 

DO 107 J=1«IJ 

M=CA+CB*TB(J)+CC*TB(J)**2+CD*TB{J)**3 

CG=,001280764*H( J) 



13 



CTr( (M-S)*TB(J) ) / ( 1+ ( M*TB ( J ) ) )*H{J) 
H(J)=H(J)-CT-CG 
2=A/(TC(J)+T0)+C 
VPC(J)=DEXP(Z) 
Z=A/(TW(J)+TO)+C 
VPW(J)=DEXP{Z) 
107 CONTINUE 

WRITE(3»3031) (TB(J) »J=1«IJ) 
WRITE(3.3032) (H(J)«J=1«IJ) 
WRITE(3»3023) (TC(J) »J=1«IJ) 
WRITE(3t302H) (TW(J) tJslf IJ) 
WRITE(3»3025) (RHC(J) »J=1»IJ) 
WRITE (3f 3026) (RHW(J) »J=1»IJ) 
WRITE{3»3027) (VPC{J) tJ=l»IJ) 
WRITE {3» 3028) (VPW(J) «J=ltIJ) 
WRITE(3t3029)VCtWW 
IF(I-I) 11,11,211 

211 WRITE(2»3015) 
WRITE(2«3016) 

READ (2. 3012) ( X (I t J ) ♦ J=l « 12 ) 
WPITE(2t3007) 
READ(2f3008)DATAOK 
IF(DATAOK.GT,0) GO TO 211 

212 WRITE<2«3017) 
WRITE{2f30l6) 

READ (2*30*^2) (SX(I»J)»J=1«12) 
WRITE(2»3007) 
READ(2»3008)DATAOK 
IF(DATAOK.GT,0) GO TO 212 

11 AWC(I)=0 
I5 = WW 

11=15/1000 
I2=(I5-I1*1000)/100 

13= ( 15-11*1000-12*100 )/l0 

14= (15-11*1000-12*100-13*10) 

DWS(I)=WSl(Il+l)+WS2(I2+l)+WS3(l3+l)+WSH{Tm-l) 

DO 108 J=1,IJ 

DC=(CON/(TC(J)-»-TO) )*( {28,9646*H(J) ) - ( 10 .S'^gS* ( V/PC ( J ) *RHC ( J) ) ) ) 

DW=(CON/(TW(J)+TO) )*( (28.96'*6*H(J) ) - (10 .9^93* ( VPW ( J ) ♦RHW( J) ) ) ) 

BY=DC*VC-DW*WW/7.93 

WRITE(3f3034)DC»DW»BY 

WC(J)=(WC( J)-(ZC( J)+ZC( J+1) )/2.0D0+BY)+DwS(I) 

AWC(I)=AWC(I)+WC(J)/AIJ 
lOfl CONTINUE 

WRITE(3f5033) (WC(J) «J=1,IJ) 

W(I)=AWC(I) 

WRITE(3»3036)W(I) 

IF(I.GT.l) 
*WRITE(3«3030) (C0|«1PID(J) « X ( I » J) «SX ( I « J ) « J=l » 12) 

S2W(I)=0 

DO 109 J=1,IJ 

S2W(I)=S2W(I) + (AUIC(I)-WC(J) )**2/(AlJ*(AlJ-1.0D0) ) 
109 CONTINUE 

IF(I-I) 112»112»12 

12 WG(I)=W(I)-W(I-1) 
S2WG(I)=S2W(I)+S2W(I-1) 



14 



1.1 SIJS2XY=0 
SllMXY = 
DO 110 J=l,12 
S?yY=(Y(J)*SX(I»J) )**2 
S1JS2XY=SUS2XY + S2XY 
SUMXY=SUMXY+X(I«J)*Y( J) 
lin COMTINUE 

DO ill J=lfl2 
XY=X(I.J)*Y(J) 
WF=XY/SUMXY 

S2XY={Y(J)*SX(I«J))**2 
WK=WF*WG( I) 
IF(Y(J)) m»15,l4 
m WY(J)=WY(J)+WK/Y(J) 
SUMWY = SUMWY + WK/Y(sJ) 
Ifi S?WF=(S2XY*(SUMXY-XY)**2+XY**2*(SUS2XY.S2XY) )/SUMXY**H 
S2WK=S2WF*WG(I)**2+S2WG(I)*WF**2 
SUS2WK(J)=SUS2WK(J)+S2WK 
111 CONTINUE 
IIP CONTINUE 
11.1 CONTINUE 
C 

C********************************* ***************************** ******* 
C*»*4c**********************«*** SECTION D **************************** 
C 

C *** SECTION D CALCULATES AND INSTRUCTS PRINTER TO wRiTE THE FOLLOWING: 
C *** FM - MOLE FRACTION OF COMPONENT J 

C *** S2FM - VARIANCE AND STANDARD ERROR OF FM FOR COMPONENT J 
C *** RELERR - RELATIVE ERROR OF FM FOR COMPONENT J 
C 

WRITE(3i3038) 
WRITE(3«300l)IHEAD 
SUS2WY=0 
DO ll*t J=l,12 
IF(Y(J)) I6»im»16 
16 S2WY(J)=SUS2WK(J)/Y(J)**2 
SIJS2WY=SUS2WY + S2WY(d) 
114 CONTINUE 

DO 115 J=1,12 

FM(J)=WY(J)/SUMWY 

S?FM(J) = (.S2WY(J)*(SUMWY-WY(J) ) **2+WY ( J ) **2* ( SUS2WY-S2WY ( J ) ) )/SuMWY 

S?FM(J)=DSQRT(S2FM(J) ) 
llfi CONTINUE 

WRITE(3»30U1) 

DO 116 J=l,12 

IF(FM(J),LE.O.ODO) GO TO 116 

RFLERR(J)=S2FM(J)/FM(J) 

IF{FM(J).GE.1.0D-03) 
*WRITE(3»30H3)COMPIO(J) »FM{J) ♦S2FM(J) »ReLeRR ( J ) .FM ( J ) .S2FM(J) 

IF(FM(J).LT.1.0D-03.AND.FM(J),GE.1.0D-06) 
*WRITE(3»304'+)C0MPID(J).FM(J)»S2FM(J) .RELeRR ( J ) .FM ( J ) , S2FM ( J ) 

IF(FM(J).LT.1.0D-06.AND.FM(J).GE.1.0D-09) 
*WRITE(3»30if5)COMPlD(J) ,FM(J) .S2FM(J) fRELERR(J) . FM ( J ) . S2FW ( J ) 

IF(FM( J) .LT.1.0D-09.AND.FM(J) •G£,1.0D-12) 
*WRITE(3.30H6)COMPID( J) .FM( J) ♦S2FM( J) «RpLeRp{J) .FM(J) .S2FM(J) 



15 



IF(FM(J).LT.1.0D-12) 
*WRITE:(3»30U7)C0MPID(J) .FM(J) fS2FM(J) «RFLFRR(J) «FH(J) ,S2FM(J) 
lift CONTINUE 

3000 FORMATdX,* ENTER HEADING OF STANDARD 66 CHARACTERS ARE ALLOWED* ) 

3001 FnRMAT(66Al) 

300? FORMATdX.'O/ ENTER NUMBER OF WEIGHING SESSIONS') 

3003 FORMAT( 'O'tTC »** ERROR •) //»T10 • t LIMITS FOR "NUMBER 0F»» 
*♦ WEIGHING SESSIONS" EXCEEDED* »//♦ IX . 7 (• ** ERRoR •)) 

3004 FORMAT(1X,»0/ ENTER NUMBER OF WEIGHINGS') 

300^ FORMATdXi '0000/ ENTER SYMBOL OF ADDITIONAL COMPONENT') 
300A FORMATdXt '0000000000,/ ENTER COMPONENT MnLECuLAR WFIGHT') 
3007 F0RMAT('7?IS DATA OK ?? YES/RETURN--NO ENtER 1') 
300fl F0RMAT(I3) 

3009 FORMAK/' SYMBOL OF ADDITIONAL COMPONENTS ' «flX f 3 ( llX » fltf ) ) 

3010 FORMAT(/' MOLECULAR WEIGHTS OF ADDITIONAL COMPONENTS ', 3( 5X»F10,6 ) ) 

3011 FORMAT(1X,»00000000./ ENTER DATA REQUESTED AT CRT') 
301? FORMAT<2X,F10,0) 

3013 FORMATdX.'OOOO/ ENTER VOLUME OF CYLINDER') 

3014 FORMATdX.'OOOO/ ENTER WEIGHT OF COUNTER BALANCE') 
301R FORMATC ENTER MOLE FRACTION OF K') 

3016 FORMATdX, '0000000000,000000000/ ENTER DaTa REQUESTED ♦) 

3017 FORMATC ENTER ERROR IN MOLE FRACTION') 

301fl FORMAT( 'ONUMBER OF WEIGHING SESSIONS = ',I3/' NUMBER OF WEIGHINGS 
*PER SESSION = ' tl0l3) 

3019 FORMATCOFOR WEIGHING SESSION NUMBER ',12*' !') 

3020 FORMATC CYLINDER WEIGHT READINGS 'tSFlCa) 

3021 FORMATC ZERO READINGS »,8F10,3) 

302? FORMATC BAROMETER READINGS •f8FlO,3) 

3023 FORMATC TEMPERATURES OF UPPER CHAMBER ♦t8Fl0,2) 

302U FORMATC TEMPERATURES OF LOWER CHAMBER »,8F10,2) 

3025 FORMATC HUMIDITIES OF UPPER CHAMBER '.SFlO.S) 

3026 FORMATC HUMIDITIES OF LOWER CHAMBER '.8F10.3) 

3027 FORMATC VAPOR PRESSURES OF UPPER CHAMBER »»8F10.3) 

302fl FORMATC VAPOR PRESSURES OF LOWER CHAMBER 'tSFlCS) 

3029 FORMATC VOLUME OF CYLINDER X WEIGHT Op COUNTER BALANCE '♦ I9» HO ) 

3030 FORMATC MOLE FRACTION AND STD. DEV. OF COMPONENTS IN ADDED GASV 
*3X.2(A*f.'= 'iE15.9C SD= '.E15.9C 2 ')/, 

*3X.2(A4«'= '.ElS.g.' SD= '»E15.9C 1 ')/» 
*3X.?(AH»'= ',E15.9.' SD= 'fE15.9C 3 ')/, 
*3X,2(A4C= 'fElS.g.' SD= 'iE15.9C 3 ')/, 
*3X,2(A4.'= ',E15.9,' SD= '»E15.9C 1 •)/» 
*3X.2(A4»'= '«E15.9C SD= 'fE15.9,' 3 ')) 

3031 FORMATC BAROMETER TEMPERATURES '»8F10,2) 

303? FORMATC CORRECTED PRESSURES •♦8F10,3) 

3033 FORMATC MASS OF CYLINDER ♦♦SFlCH) 

3034 FORMAT ( ' DC DW BY » t 3E3 2.5) 

303«> FORMAT( '0' .7C**FRR0R ')//T20.' WW-NOT GlVpN • , // » IX » 7 C **ERR0R ')) 

3036 FORMATC AVERAGE OF CYLINDER MASSES •♦F10.<+) 

3037 F0RMAT(2X»A*t) 
303fl FORMATdHl/) 

3039 F0RMAT{2X.I1) 

3040 F0RMAT(2Xd't) 

3041 FORMAT (//.35X» • STANDARD ' dOX » ' RELATIVE • dOX » 'MOLE' . lAXC STANDARD ' / 
*1?X» 'CONCENTRATION' d IX. 'ERROR' »13X. 'ERROR' » lOX t 'FRACTION' . 

*17X« 'ERROR' ) 

3042 FORMAT(2X.D20,10) 



16 



SO'*.-^ FORMAK 'O' ,3X,A^, 2PF15.5»' % *, 2PF15.5.' % S 2PF15,5»» « <• 

* ,0PE16.10» • ) • »«SX» M • fOPEie.lO* • ) • ) 

30tft| FDRMAK •0» ♦3X»A'+. 6PF15.5»» PPM», 6PF15.5»» PP^lN 2PF15.5»» SB (• 

* ,0PE16.10»M»»f5Xt»'(» ♦0PE16.10f ♦ ) • ) 

30tt«S FORMAK 'O* ,3X.A4, 9PF15.5»» PPB», 9PF15,5»» PPR'» 2PFl5.5.» 55 (• 

* .0PE16.10* • ) ♦ »5X» M • »0PE16,10» » ) • ) 

304^ FnRMAK 'O* ,3X«A*+,12PF15,5»» PPT • , 12PF15 .5 ♦ • PPtS 2PF15.5t» % (• 

* ,0PE16.10» ♦ ) • »5Xt • ( • »0PE16.10» • ) • ) 

3047 FnRMAK 'O' ,3X,A1,5Xf lPEl5.9f5X«lPEl5,9,2pFl3.5,» % (• 
*.0PE16.10t» ) • t5X, M ♦tOPE16.10f • )♦) 
WRITE(2.30'+8) 
304ft FORMAT(lXt«0/ ?7 ANOTHER CALCULATION ?? YES/ENTER 1--N0/RETURN* ) 
READ(2«3039) LOOP 
IF(L00P,GE,1) GO TO 100 
999 STOP 
END 
/* 



17 



APPENDIX B.— FLOW CHART FOR COMPUTER PROGRAM PRISTD 

Program calculates compositions and error of gravimetric primary 
standard gas mixtures. 

Section A: Specifies and assigns variables and most of the 
constants used in the program. 



( START J 



I 



REAL; I^f^EGER; DOUBLE PRECISION variables specified: 
M; COMPID, DATAOK, WW, VC; A, C, M, S, CA, CB, CC, 
CD, CO, CT, Z, RELERR, AI J , WY, X, XY , Y, ZC, CON, 
TO, RHW, AWC, BY, TB, DC, DW, DWS , FM, H, RHC , S2FM, 
S2W, S2WF, S2WG, S2WK, S2WY, S2XY, SUMWY, SUMXY , 
SUS2WK, SUS2WY, SUS2XY, SX, TC, TW, VPC, VPW, W, WC, 
WF, WG, WK, WSl, WS2, WS3, WS4 



I 



DIMENSION of arrays specified: WSl(ll), WS2(10), 
WS3(10), WS4(10), IHEAD(66), JJ(8), H(7), RHC(7), 
RHW(7), TC(7), TW(7), VPC(7), VPW(7), WC(7), ZC(8), 
S2WG(8), WY(12), AWC(8), DWS(8), W(8), S2W(8), WG(8), 
X(8,12), SX(8,12), FM(12), Y(12), TB(8), S2WY(12), 
S2FM(12), SUS2WK(12), C0MPID(.12), RELERR(12) 



I 



Data for following constants specified: A, C, S, CA, 
CB, CC, CD, WSl, WS2, WS3, WS4, COMPID 



I 



DATA FOR 

yd) thru y(9) 

assigned 



I 



TO AND CON 
ASSIGNED 




18 



Section B: Requests input data for the following; 
IHEAD, MAXI, JJ, COMPID, Y. 




/^ ^ / Read com- 

N 100 j W posed head- 

V y \ ing (IHEAD) 



'Read maxi- 
mum number 
of weighing 
sessions (MAXI) 




I Read number of weighings per / 
/ session (JJ) / 

V 

Read symbol (s) and molecular 
weight(s) of additional 
component (s) 



s 



Assign; 
SUS2WK(J)=0 
S2WY(J)=0 
WY(J)=0 
for J- 1.2. . 



12 



s 



Assign: 
SUMWY=0 
WG(1)=0 
S2WG(1)=0 



5 



Write: IHEAD, 
MAXI, symbol (s) 
and molecular 
weight(s) of 
additional com- 
ponent (s)j. 



W Section) 



19 



Section C: Requests input data and/or calculates the following for 
each weighing session: WC , ZC, TB , H, RHC , RJ-IVJ, TC , TW 
VC, WW, VPC, VPW, X, SX, DVJS, DC, DW, BY, AWC , S2W, WG, 
S2v^G, XY, S2XY, SUS2XY, SUMXY, WF , \K, WY, SUtWY, S2WF, 
S2WK, and SUS2WK. 




Read data for weighing session: 
WC - Balance weight measurements 
ZC - Balance zero readings 
TB - Barometer temperature readings 



H 



Barometer readings 



RHC - Relative humidities, balance upper chamber 
RHW - Relative humidities, balance lower chamber 

TC - Temperature upper chamber 

TW - Temperature lower chamber 

VC - Weighing cylinder displacement volume 

WW - Counterbalance weight 




Read WW - 
counterbalance weight 




-[> 



Write 
error 
statement 



— C/210J 



SL 



Write input 
data: weighing 
session I, WC(J) 
ZG(J), H(J) 



20 



Section C, continued; 



± 



J - 1,2, ...,IJ 
(IJ = JJ(I)) 



I 



Calculate Barometric Pressure, H(J): 

M = CA + CB * TB(J) + CC * TB(J)**2 + CD * TB(J)**3 

CO = 0.001280764 * H(J) 

CT = ((M-S) * TB(J))/(H-(M * TB(J))) * H(J) 

H(J) = H(J) - CT - CG 



I 



Calculate Vapor Pressure of Water for 
upper chamber, VPC (J); and lower 
chamber VPW(J) 

Z = A/(TC(J) + TO) + C 

VPC(J) = DEXP(Z) 

Z = A/(TW(J) + TO) + C 

VPW(J) = DEXP(Z) 



I 



J = J+1 



£^ 



No 



Write input data, 
TB(J), TC(J), TW(J), 
RHC(J), RHW(J). 
For J =- 1,2, ...,JJ 




Write calculated 
values H(J), VPC(J) 
VPW(J), For J - 1.2, 



.JJ 



1 



Write input 
data VC and 
WW. 



21 



Section C, continued: 




'Read mole fraction 
of components in 

weighed gas, X(I,.J); 
for J = 1.2 12 



I 



'Read error deviation 
of X, SX (I, J) 
for J - 1,2, ...,12 



I 



Assign average 
mass of cylinder 

AWC(I) = 0, 
and 15 = WW 



I 



<F 



11 


= 15/1000 












12 


= (15 - 


- 11 


* 


1000)/100 






13 


= (15 - 


- 11 


* 


1000 - 


- 12 * 


100)/10 




14 


= (15 - 


- 11 


* 


1000 - 


- 12 * 


100 - 13 * 


10) 



I 



Calculate correction for inaccurracy 
of balance weights, DWS(I): 
DWS(I) = WS1(I1+1) + WS2(I2+1) 
+ WS3(I3+1) + WS4(I4+1) 



22 



Section C, continued: 



Assign: 
W(I)=AWC(I) 



J 



<y 



i 



J - 1,2, ...,IJ 
(IJ - JJ(I)) 



I 



Calculate density of air in upper 

charabe r , DC : 

DC = (CON/(TC(J) + TO)) * ((28.9646 R 

* H(J)) - (10.9493 * (VPC(J) 

* RHC(J)))) 



5 



Calculate density of air in lower 

chamber, DW: 

DW = (CON/(TW(J) + TO)) * ((28.9646 

* H(J)) - (10.9493 * (VPW(J) 

* RHW(J)))) 



5 



Calculate buoyancy correction, BY: 
BY = DC * VC - DW * WW/ 7. 93 



5 



V/rite calculated 

values 

DC, DW, BY 




Calculate mass of cylinder, 

WC(J), and average mass of 

cylinder, AWC(I): 

WC(J) = (WC(J) - (ZC(J) + ZC(J+1))/2.0D0 

+ BY) + DWS(I) 
AWC(I) = AWC(l) + WC(J)/AIJ 



Yes 




23 



Section C, contiaued: 



Write calculated 
values WC(J), 
W(I) 




Write input 
data X(I,J), 
SX(I,J), for 
J = 1,2,.. ..12 



Assign: 
S2W(I) = 



SL 



J " 1.2 IJ 

(IJ = JJ(I)) 



I 



Calculate standard 
error of weighing 
session; S2W(I): 

S2W(I) = S2W(I) + (AWC(I) 
- WC(J))**2/(AIJ 
* (AIJ - l.ODO)) 



<y 




24 



Section C, continued 



i 



Calcu 


Late mass 


of added gas, 




WG(I) 






WG(I) 


= W(I) 






-W(I- 


-1) 











V 



Calculate error 
propagation of standard 
error of weighings, 

S2WG(I): 
S2WG(I) = S2W(I) 

+ S2W(I-1) 



Assign: 
SUS2XY = 
SUMXY = 



5 



J - 1,2, ...,12 



I 



Calculate error propagation of 
product, Y(J) * SX(I,J), S2fflf: 
S2XY = (Y(J) *SX(I,J))**2 



I 



Calculate summation of S2XY'S 
for weighing session, SUS2XY: 
SUS2XY = SUS2XY + S2XY 



I 



Calculate summation of product! 
of X(I,J) * Y(J), SUMXY: 
SUMXY = SUMXY + X(1,J) * Y(J) 




25 



Section C, continued: 



J - 1,2, ...,12 



Calculate product of X(I,J) * Y(J) 
for session per component, XY: 
XY = X(I,J) * Y(J) 



I 



Calculate weight fraction of 
compoaent , WF: 
WF = XY/SUflXY 



^ 



Calculate error propagation of product 
Y(J) * SX(I,J), S2XY: 
S2XY = (Y(J) * SX(I,J))**2 



5 



Calculate grams of component J, 

WK: 

WK = WF * WG(I) 



Yes 




No 



Calculate moles 

of each component 

WY(J): 

WY(J) = WY(J) + WK/Y(J) 



5 



Calculate summation 
of moles of all compo- 
nents, SUMWY: 
SUMWY = SUMWY + WK/Y(J) 



^> 



Calculate error propagation of 
WF(J) for component J, S2WF: 
S2WF = (S2XY * (SUMXY - XY)**2+XY**2 
* (SUS2XY - S2XY))/SUMXY**4 



I 



26 



Section C, continued 



i 



Calculate error propagation of 
product WF * WG(I), S2WK: 
S2WK = S2WF * WG(I)**2 + S2WG(I) 
* WF**2 



5 



Calculate summation of error of 
grams of component J,SUS2WK(J): 
SUS2WK(J)= SUS2WK(J) + S2WK 




27 



Section D: Calculates and instructs printer to write the following: 
inole fraction of each component (FM) , standard error, and 
relative error for each FM. 




Write 
IHEAD at 
top of page. 



^ 



Assign: 
SUSWY = 



5 



I J - 1.2,...,12| 




Calculate summation of 

error of coraponent J, 

S2WY(J): 

S2l^(J) =SUS2WK(J)/Y(J)**2 



5: 



Calculate summation of 

error of all components, 

SUS2l^rY: 

SUS2WY = SUS2WY + S2^^rY(J) 




28 



Section D, continued; 



i 



J =« 1.2 12 



5 



Calculate total mole 
fraction of component 
J, FM(J): 
FM(J) = WY(J)/SUm/Y 



I 



<F 



Calculate error propagated of 
FM(J) for component J, S2FM(J): 
S2FM(J) = (S2WY(J) * (SUMWY - WY(J)) 

**2 + WY(J)**2 * (SUS2V7Y 

- S2l7Y(J)))/SUm^JY'''*4 



I 



Calculate standard 
error of FM(J), S2FM(J): 
S2FM(J) = DSQRT(S2FM(J)) 




Write column headings: 
CONCENTRATION, STANDARD 
ERROR, RELATIVE ERROR, 
MOLE FRACTION, STANDARD 
ERROR 



29 



Section D, continued 



i 



J = 1,2,....12 



Yes 




Calculate, relative 
error, relerr(j): 

Relerr(J) = S2FM(J)/ 

FM(J) 



10-6 < FM(J) <10-3>^^M> S2FM(J) RELERR(J), 
_ V >» Mu^ 1/ p„(j)^ S2FM(J), 




Write: 

COMPID(J), FM(J), 
S2FM(J), RELERR(J), 
FM(J), S2FM(J), 
% range 



-^ 



Write: 
COMPID(J), FM(J) 



ppm range 



^> 



Write: 

COMPID(J), FM(J) 
jvJS2FM(J), RELERR(J),L_r>^ 
"^ FM(J), S2FM(J), ■'^ 

ppb range ^ 



Write: 

COMPID(J), FM(J), 
S2FM(J), RELERR(J) 
FM(J), S2FM(J), 
ppt range 



-> 



Write: COMPID(J), 

FM(J), S2FM(J), 
JxJ RELERR(J), FM(J), Ijv, 
^S2FM(J), ' '^ 

Exponential 

Notation 




30 



APPENDIX C. —SAMPLE CALCULATION OF GRAVIMETRIC PRIMARY STANDARD MIXTURE 



The following data were obtained for a 
methane-in-nitrogen mixture blended to 
contain approximately 3% methane. Three 
weighing sessions consisting of three 
weighings each were conducted. Inclusion 
of the chemical symbols and molecular 
weights for three additional components, 
ethane, propane, and isopentane, was nec- 
essary. The external cylinder volume was 
previously determined gravimetrically by 
a water displacement procedure. Purity 
of the gases was determined by analyses 
of the 12 listed components. 

Requisite computation data for the 
gravimetric mixture were obtained and 
recorded from various instruments. The 
weight and mass determination data were 
acquired from a high-capacity (12-kg) 
substitution balance sensitive to ±1 mg. 
Temperature, relative humidity, and bar- 
ometric pressure data were obtained from 
bimetal centigrade thermometers accurate 
to ±0.3° C, direct-reading hygrometers 
accurate to ±1.5%, and a mercurial ba- 
rometer accurate to ±0,05 mm Hg, 
respectively. 

Sample Input 

I, Program identification and control 
parameters. 

Item 1 (composed heading, IHEAD) : 
S-374, CYL, No, H-84846, 3% 
CH4 IN N2, 12/14/1979 

Item 2 (No. of weighing sessions, 
MAXI): 
3 

Item 3 (No, of weighings per ses- 
sion, JJ(I)): 
3 
3 
3 

Item 4 (additional component chem- 
ical symbol and molecular or 
atomic weight, COMPID and 
(Y(J)): 
C2H6 

30,07012 
C3H8 

44,09721 
I-C5 
72.15139 



II, Mass and buoyancy determination data 
for each weighing. 



Session 1 



Session 2 



Session 3 



ITEM 1 (WEIGHT READINGS, WC(J) , g) 



4333,484 


4342,566 


4779,617 


4333,486 


4342,578 


4779,629 


4333,487 


4342,592 


4779,635 



ITEM 2 (ZERO 


BALANCE READINGS, 


ZC(J), g) 


0,355 


0,416 




0.487 


,359 


,428 




.500 


.363 


.435 




.504 


.367 


.447 




.508 



ITEM 3 (BAROMETER TEMPERATURE READINGS, 
TB(J), °C) 



20.5 


22.3 


22.8 


20.5 


22.5 


23.0 


20.6 


22.7 


23.1 



ITEM 4 (BAROMETRIC PRESSURE READINGS, 
H(J), mm Hg) 



676.95 


675.85 


674.80 


676.90 


675.80 


674.70 


676.85 


675.85 


674.60 



ITEM 5 (RELATIVE HUMIDITY READINGS OF 
BALANCE UPPER CHAMBER, RHC(J)) 



0.190 


0.175 


0,185 


.195 


.185 


.195 


.200 


,195 


.200 



ITEM 6 (RELATIVE HUMIDITY READINGS OF 
BALANCE LOWER CHAMBER, RHW(J)) 



0.125 


0.130 


0.130 


,125 


.130 


.135 


.125 


.130 


.135 



ITEM 7 (TEMPERATURE READINGS IN BALANCE 
UPPER CHAMBER, TC(J), °C) 



21.6 


22.6 


23.7 


21.6 


22.7 


23,7 


21.6 


22.8 


23,8 



ITEM 8 (TEMPERATURE READING IN BALANCE 
LOWER CHAMBER, TW(J), °C) 



20,5 
20.5 
20.6 



21.3 
21.4 
21.4 



21.9 
22.0 
22.0 



ITEM 9 (DISPLACEMENT VOLUME MEASUREMENT 
OF CYLINDER, VC, mL) 



4220 




J 4220 




1 4220 


ITEM 


10 


(COUNTERBALANCE 
CYLINDER, WW, g) 


WEIGHT OF 


4333 




1 4342 




1 4779 



III. Composition data of gases, 



31 





Mole fraction | Standard error 


Mole fraction | Standard error 




Methane 


Nitrogen 


He 


0.00005 
.00005 
.00005 
.00080 
.995550 
.00005 
.00010 
.00005 
.0 

.002300 
.00080 
.00020 


0.00005 
.00005 
.00005 
.00005 
.000165 
.00005 
.00005 
.00005 
.0 

.000069 
.00005 
.00005 


0.000002 
.0000012 
.0000047 
.99952 
.00005 
.000026 
.00020 
.00005 
.0 

.00005 
.00005 
.00005 


0.000002 


H2 


.0000012 


NE 


.0000047 


N2 


.00013 


CH4 


.00005 


02 


.000026 


AR 


.00005 


C02 


.00005 


He3 


.0 


C2H6 


.00005 


C3H8 

I-C5 


.00005 
.00005 



32 



NO. H-84ei|6. 358 CHH IM N2, 12/14/1979 



numrer of weighing sessions = 3 
niimrer of ijeighings per session = 3 



symrol of additional components 

molfciilar weights pf additional components 



CPH6 
30.n70l?0 



C3H8 
141*, 097210 



I-C5 
72.l5i390 



FOR WEIGHING SESSION MUMBER 1 : 

CYLINDER WEIGHT READIriGS il333.'»fi'+ 4333. Hfl6 4333. H87 

ZERO RFAPTNGS 0.3 = 5 0.359 0.363 0.367 

BAROMETER READINGS 676.950 676.900 676,850 

BAROMETER TEMPERATURES 20.50 20.50 20.60 

CORRECTED PRESSURES 673.8?7 673.777 673.716 

TEMPERATURES OF UPPER CHAMBER 21.60 21.60 21.60 

TEMPERATURES OF LOWER CHAMBER 20.50 20.50 20.60 

HUMIDITIES OF UPPER CHAMBER 0.190 0,195 0.200 

HUMIDITIES OF LOWER CHAMBER 0.125 0.125 0.125 

VAPOR PRESSURES OF UPPER CHAMBER 19.346 19.3*16 19.3H6 

VAPOR PRESSURES OF LOWER CHAMBER IS.OflS 18.085 18.196 

VOLUME OF CYLINDER X WEIGHT OF COUNTER BALANCE tjSPO U333 

DC DW RY 0.105q6F-02 0.106H«tE-02 0.38a99E + 01 

DC nw RY 0.10595F-02 0.106t3E-02 0.38893E + 01 

DC DW BY 0.10593E-02 0.10639E-02 0.388fl9E + 01 

MASS OF CYLINDER t337.0722 "+337.0696 '♦337.0662 

Average of cylinder masses 4337.0693 

FOR weighing session NUMBER 2 : 

CYLINDER WEIGHT READINGS 4342.566 4342.578 4342.592 

ZERO READINGS 0.416 0.428 0.435 0.447 

BAROMETER REAniNGS 675.650 675.800 675.850 

BARnMETER TEMPERATURES 22.30 22.50 22.70 

CORRECTED PRESSURES 672.534 672.463 672.491 

TEMPERATURES OF UPPER CHAMBER 22.60 22.70 22.80 

TEMPERATURES OF LOWER CHAMBER 21.30 21.40 21.40 

HUMIDITIES OF UPPER CHAMBER 0.175 0.185 0.195 

HUMIDITIES OF LOWER CHAMBER 0.130 0.130 0.130 

VAPnR PRESSURES OF UPPER CHAMBER 20.560 20.685 20.811 

VAPnR PRESSURES OF LOwER CHAMBER 18.994 19.111 19.111 

VOLUME OF CYLINDER X WEIGHT OF COUNTER BALANCE 4220 4342 

DC DW RY 0.10540F-02 0.10593E-02 0.38679E + 01 

DC.....DW BY 0.10534F-02 0.10589E-02 0.38656E + 01 

DC nw BY 0.10530E-n2 0.10589E-02 0.38637E + 01 

MASS OF CYLINDER 4?546.o674 4^46.0676 4346.0702 

AVERAGE OF CYLINDER MASSES 4346.0684 

MOLE FRACTION AND STD. DEV. OF COMPONENTS I^: aDDED GAS 

HE = 0.500000000E-04 SD= . 500000000E-04 D H? = . 500000000E-04 S0= . 500000000E-04 

IMF = 0.500000000E-P4 SD= . 500000000E-04 3 N? = .flOOOOOOOOE-03 SD= . 500000000E-04 

CH4 = 0.995550000E+00 SD= . 165000000E-03 D 0? = . 500n00000E-04 SD= .500000000E-04 

AR = O.lOOOOOOOOE-03 SD= . 500000000E-04 D Co2 = . 5n0O0000OE-04 SD= . 500000000E-04 

HE3 = O.OOOOOOOOOE+00 SD= . OOOOOOOOOE+00 ] C?H6= . 230000000E-02 SD= .690000000E-04 

C3Hfl= 0.80000nOOOE-03 SD= . 500000000E-04 3 I-C5= . 2O0n00000E-03 Sn= 0.500000000E-04 



FOR WEIGHING SESSION NUMBER 3 ! 

CYLINDER WEIGHT READINGS 4779.617 4779.629 4 

ZERO READINGS 0.4«7 0.500 

BAROMETER READINGS 674.800 674.700 

BAROMETER TEMPERATURES 2?.fl0 23.00 

CORRECTED PRESSURES 671.435 671.314 

TEMPERATURES OF UPPER CHAMBER 23.70 23.70 

TEMPERATURES OF LOWER CHAMBER 21.90 22.00 

HUMIDITIES OF UPPER CHAMBER 0.1fl5 0.195 

HUMIDITIES OF LOWER CHAMBER 0.130 0.135 

VAPOR PRESSURES OF UPPER CHAMBER..,.. 21.973 21.973 

VAPOR PRESSURES OF LOwER CHAMBER 19.703 19.824 

VOLUME OF CYLINDER S, WEIGHT OF COUNTER BALANCE 4220 4779 

DC DW BY 0.104fllE-02 0.10554E-n 

DC nw RY 0.1 0478*- -02 0.1054 8E-0 

DC nw RY 0.10472t-02 0.10546E-0 

MASS OF CYLINDER 4782.97^5 47fl2.9760 47 

AVERAGE OF CYLINDER MASSES 4782. 97$1 

MOLE FRACTION AND STD. DEV. OF COMPONENTS IN ADnED GAS 

HF = n.20000000nE-05 SD= 0.200POOOOOE-05 D H9 = . 1?OOOOOOOE-05 

NF = n.47000nOOOE-05 SD= n.470000000E-05 3 N? = . 999520000E+00 

Ch4 = 0.5n0000000E-04 SD= . 5O0nO00OOE-04 : 0? = 0.260000000E-04 

AR = 0.200000000E-n3 SD= . 500000000E-04 3 Co2 = .500000000E-04 

HE3 = O.OOOOOnOOOE+nO SD= O.OOOnOOOOnE+00 3 C2H6= 0.5nOOOOOOOE-04 

C3Hfi= 0.500000000E-P4 SD= . 500000000E-04 3 I-C5= . 5nOOOOOOOE-04 



779.635 

0.504 0. 
674.600 

23.10 
671.203 

23.80 

22.00 

0.200 

0,135 
22.106 
19.824 

2 0.37870E+01 
2 0.37860E+01 
2 0.37836E+01 
82,9756 



SD= 0,120000000E-05 
SD= 0.130000000E-03 
SD= 0.260000000E-04 
SD= 0.500000000E-04 
SD= 0.500000000E-04 
SD= 0.500000000^-04 



S-S?"*. CYL. NO. H-84846. 3!S CH4 IN N2, 12/14/1979 



33 





COMCENTRflTlON 


STANDARD 
ERROR 


relative: 

ERROR 




HOLE 
FRACTION 


STANDARD 
ERROR 


HE 


3.65886 


PPM 


2.59115 


PPM 


70.91865 


% 


(0.3658857826E-05) 


(0.2591153849E-05) 


H2 


2.88651 


PPH 


2.08040 


PPM 


75.07309 


% 


(0.?886508594E-05) 


(0.20a0395965E-05) 


NE 


6.26554 


PPM 


4.85536 


PPM 


77.49309 


« 


(0.6265536484E-05) 


(0.4855358091E-05) 


m2 


96.50008 


% 


0.01179 


% 


n.01?22 


% 


(0.9650007781E+00) 


(0.1179197625E-03) 


rHu 


3.tt5t? 


% 


0.00494 


% 


0.14325 


% 


(0.3t454l761lE-01) 


(0.4935671702E-04) 


n2 


26.82933 


PPM 


25.15933 


PPM 


93.77?45 


X 


(0.?68293347aE-04) 


(0.2515932828E-04) 


flR 


196.54328 


PPM 


48.27952 


PPM 


24.56432 


56 


(0.)965432775E-03) 


(0.4e27552233E-04) 


r02 


1+9.99981 


PPM 


48.29654 


PPM 


96.59344 


% 


(0.4999981174E-04) 


(0.4e29653585E-04) 


C2Hf, 


127.75913 


PPM 


48.32145 


PPH 


37.82231 


% 


(0.1277591253E-03) 


(0.4832144626E-04) 


r3Hfl 


75.91958 


PPM 


48.29515 


PPH 


63.61356 


% 


(0.7591958294E-04) 


(0.4829515294E-04) 


i-cs 


55.1P377 


PPM 


48.29382 


PPH 


87.51454 


% 


(0,5518376598E-04) 


(0.4829381626E-04) 



34 



APPENDIX D. —NOMENCLATURE 




AWC(I) 



Definition 

Constant In the vapor pressure of water determination. 

Program control parameter, equal to number of weighing 
measurements per weighing session. 

Average mass of cylinder for a weighing session, equa- 
tion 10. 



BY 

C 

CA 

OB 

CC 

CD 

CG 

COMPID(J) 

CON 
CT 



DATAOK 



Buoyancy correction factor, equation 1. 

Constant In the vapor pressure of water determination. 

Constant In the mean coefficient of cubical expansion 
of mercury determination (7). 

Constant In the mean coefficient of cubical expansion 
of mercury determination (7^). 

Constant In the mean coefficient of cubical expansion 
of mercury determination (_7 ) . 

Constant In the mean coefficient of cubical expansion 
of mercury determination (_7 ) , 

Acceleration of gravity correction factor (8^), 

Program alphanumeric array of chemical symbols for 

nine normally used components. 

Factor to correct density of air to standard 
conditions. 

Factor to correct barometric pressure measurement for 
temperature variations. 

General expression for determination of air density, 
equation 2, 

Program control parameter to correct data entry 
errors 



DC 
DW 

DWS(I) 

FM(J) 



Density of air determination In balance upper chamber. 

Density of air determination In balance lower chamber. 

Factor to correct cylinder mass measurements for Inac- 
curacies of utilized balance weights. 

Mole fraction determination for a component In the 
final mixture, equation 4, 



35 



Fortran Symbol Text Symbol Definition 

H(J) P Barometric pressure measurement. 

11 Program parameter equal to quantity of utilized kilo- 

gram balance weights in a mass measurement. 



12 



Program parameter equal to quantity of utilized hecto- 
gram balance weights in a mass measurement. 



13 



Program parameter equal to quantity of utilized deka- 
gram balance weights in a mass measurement. 



14 



15 



Program parameter equal to quantity of utilized gram 
balance weights in a mass measurement. 

Program parameter equal to nominal mass measurement of 
cylinder. 



IHEAD(I) 



Program parameter equal to composed alphanumeric head- 
ing of program composed by user. 



IJl 



Program parameter equal to quantity of balance zero 
measurements per a weighing session. 



IJ 



JJ(I) 



LOOP 



Program parameter equal to quantity of cylinder mass 
measurements per a weighing session. 

Program parameter equal to quantity of cylinder mass 
measurements per a weighing session. 

Program control parameter required to initiate a sub- 
sequent calculation. 



Mean coefficient of cubic thermal expansion of mercury 
determination (2^). 

Molecular weight of air. 



MAXI 



Program parameter equal to quantity of weighing 
sessions. 






Molecular weight of water. 

Barometric pressure at standard conditions, 



RELERR(J) 

RHC(J) 

RHW(J) 



Mole fraction relative error determination of a 
component. 

Relative humidity measurement in balance upper 
chamber. 

Relative humidity measurement in balance lower 
chamber. 



36 



Fortran Sjonbol Text Symbol Definition 

S Linear coefficient of thermal expansion of the barom- 

eter scale. 



S2FM(J) 



'I 



Mole fraction standard error variance determination of 
a component in the final mixture, equation 13. 



SUMWY 



N 12 
E IK 
3=1 1=1 -' 



i»3 



Summation of moles for all components in all weighed 
gases. 



SUMXY 



12 



Summation of products of mole fraction content and re- 
spective atomic or molecular weight of all components 
in a weighed gas. 



SUS2WK(J) 



% 



Total mass standard error variance determination of 
component in the final mixture, equation 17. 



SUS2WY 



i=l Mi 



Summation of standard error variance of total moles 
for all components in the final mixture. 



SUS2XY 



E S2 
1=1 Zi 



Summation of standard error variance of products of 
mole fraction content and respective atomic or molec- 
ular weight of all components in the weighed gas. 



S2WF 



Si 



Weight fraction standard error variance determination 
of a component in the weighed gas, equation 19. 



S2WG(I) 


S2 


S2W(I) 


%+1 


S2W(I-1) 


% 


S2WK 


%. 


S2WY(J) 


% 



Mass standard error variance determination of a weigh- 
ed gas, equation 23. 

Mass standard error variance determination of the cyl- 
inder for next weighing session, equation 24. 

Mass standard error variance determination of the cyl- 
inder for a weighing session, equation 24. 

Mass standard error variance determination of a compo- 
nent in the weighed gas, equation 18. 

Total moles standard error variance determination of a 
component in the final mixture, equation 16. 



SX(I,J) 



Sx. 



Analytical standard error of a component in the weigh- 
ed gas. 



S2XY 



Product of mole fraction content and respective atomic 
or molecular weight standard error variance determin- 
ation of a component in the weighed gas, equation 22. 



37 



Fortran Symbol Text Symbol 



TB(J) 




TC(J) 


T 


TW(J) 


T 


TO 


T. 


VC 


V, 



VPC(J) 


Vp 


VPW(J) 


Vp 




Vw 


WC(J) 


% 


WC(J) 


\ 


WF 


Fi 


WG(I) 


Wj 


W(I) 


^+1 


W(I-l) 


\ 



WK 



WS1(I1+1) 



WS2(12+1) 



WS3(I3+1) 



'lO 



Definition 

Atomic or molecular weight standard error variance of 
a component in the weighed gas. 

Ambient room temperature measurement. 

Temperature measurement in balance upper chamber. 

Temperature measurement in balance lower chamber. 

Temperature conversion factor, "C to K. 

Cylinder displacement volume measurement. 

Molar volume of ideal gas at standard conditions. 

Vapor pressure of water determination for balance 
upper chamber, equation 3. 

Vapor pressure of water determination for balance 
lower chamber, equation 3. 

Volume of utilized weights determination. 

Mass determination of cylinder, equation 11. 

Nominal mass measurement of the cylinder. 

Weight fraction determination of a component in the 
weighed gas, equation 7. 

Mass determination of the weighed gas, equation 9. 

Average mass determination of the cylinder for a 
weighing session, equation 10. 

Average mass determination of the cylinder for a 
previous weighing session, equation 10. 

Mass determination for a component in the weighed gas, 
equation 6. 

Program parameter equal to accumulated correction fac- 
tors of utilized kilogram balance weights in a mass 
measurement . 

Program parameter equal to accumulated correction fac- 
tors of utilized hectogram balance weights in a mass 
measurement . 

Program parameter equal to accumulated correction fac- 
tors of utilized dekagram balance weights in a mass 
measurement . 



38 



Fortran S3aabol 
WS4(I4+1) 

WW 



Text Symbol 



WY(J) 


^i,j 


WY(J) 


Mi 


X(I,J) 


Xi 



Definition 

Program parameter equal to accumulated correction fac- 
tors of utilized gram balance weights in a mass 
measurement . 

Nominal mass measurement value truncated to the near- 
est gram. 

Moles of a component in the weighed gas, equation 5. 

Total moles of a component in the final mixture. 

Mole fraction content of a component in the weighed 



XY 

Yd) 

Y(2) 
Y(3) 
Y(4) 
Y(5) 
Y(6) 
Y(7) 
Y(8) 
Y(9) 
Y(J) 
Z 

ZC(J) 
ZC(J+1) 



'r+1 



Product of mole fraction content and atomic or molec- 
ular weight of a component in the weighed gas , equa- 
tion 8 and 20. 

Atomic weight of helium. 

Molecular weight of hydrogen. 

Atomic weight of neon. 

Molecular weight of nitrogen. 

Molecular weight of methane. 

Molecular weight of oxygen. 

Atomic weight of argon. 

Molecular weight of carbon dioxide. 

Atomic weight of helium-3. 

Atomic or molecular weight of additional components. 

Natural logrithm determination of vapor pressure of 
water calculation. 

Balance zero measurement. 

Next balance zero measurement. 



T!rU.S. GPO: 1985-505-019/20,082 



IT.-BU.OF MINES,PGH.,PA. 28032 



D DD 

2 Q- O Q O O 

sr^i." f 

Q 5 - — O 

«i n in 

- 2" 3 -^ ^ ;c 

3 Q Q — -I- « 

!±: to — Q -1 O- 
n (t> 3 t/i (I <v 
Q • «Q rt n ^ 

•"" ? ^' 3 ™ 
re j^ = _► 

U) < -• 




5° 



— m ' ' 

z z > 

H -I 2 

± O o 



5> 

m o 

X 

o 



^0" 




': -^^^^ 



^ .>V^\ \^' ;a^-/ %,.*■ •■ 






V /\ • 



■^^. 



: ^^^'^^^ ^^le; A'^^^ \ 






4;-' vV^^* ^ 



^ '^V' '^> 



"ir %?< "; 











^*^°- 




o V 



"^Mr.<i 
















0- -% ^^^XT^ .v'V 

■N^ - " O . *C -„ 








^'^'^ 



0^ .0°^"*^ *0, ^^'^ 



XP-TI 



.' ^^'\'M^/ /\^':^SA'^'^^. 




^^-^^^ 










^^0^ o 







* A 




i- \.# •■ 









* 



r ^r^^ =. 







o X.^'^ o^ 






















oL% ^ 



^/v>*\-^i«i^X./ /Mfe^ ><..*^ .-^^C^". V^** /Jfe-v %/ 4 









r^.'* '^ 






«^c 








5"^. 



••/'-..-•. 







"oV 



Ao^ 








^^ ^-^..^^' ;aK^ ^^..^^ .«i^^o -^.^/^ /^g. \/ ; 









,/% 






>;- 



'.- .-!••' °-. 












^^^^. 



,v V. 



'i.> '«. 


















v^^ 










;* .o'5 



^"-"cK 




,4q 







^^-n^. 







Ao, 







^,* -^^ ^* 






%/^^' 



^^^>. °; 














.^ <^^^ 







>*"^'s:^.....V"^'^^.^.>:' 




/ aK 



^\ "^-^..^^ *^^ 






V •>,^<>' 



%, 








«^ q. 



,% 'e^ A^ ' /^Va". '\ J" ♦^^^iK'. 'e. A^ ' ^'^ 



^j^«b^ 



•^^^^ 







rZ:^s'^:€.y,><^-y.^^:^:/.^^^^ 












\,^^ 
.1>\ 



























•7* 







^^-n.. 











.^^"o, 



^. '.mm, ^^'\ o, 







V.>* :^i£', *v.s*' ••• 

















^rfX * o - o ' O. V 










^^\ ^ 



.% '^ 




^ " ^^ 







^^-^. 




^Mr.'i 







o > 



^ ^0 













^^'% 



^^^^v :, 
■3^. 




'bV" 








,^^ > 



V 






^^-n^. 









. .*^"*. 






5- Vk '.^ili^" .^^^'^ 









